We consider economic growth in the presence of a minimal survival consumption level when preferences are lexicographic giving highest priority to the survival of the current and then all future generations. Knowledge of production is incomplete so future output made possible by current saving must be estimated. The resulting capital accumulation path is compared with the inter-temporally optimal one with full knowledge of the production function. Although previous results with the standard utility function show that for sufficiently strong discounting the adaptive strategy converges to the optimal path, in the present case in several scenarios the effect of adaptive economizing under incomplete information is drastic leading to demise of the economy although long-run survival would be possible. (C) 2006 Elsevier B.V. All rights reserved.